Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods

Akihiko Nishimura, David B. Dunson, Jianfeng Lu

Research output: Contribution to journalArticlepeer-review

Abstract

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters through the embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding numerical solver. The proposed solver is the first of its kind, with a remarkable ability to exactly preserve the Hamiltonian. We apply our algorithm to challenging posterior inference problems to demonstrate its wide applicability and competitive performance.

Original languageEnglish (US)
Pages (from-to)365-380
Number of pages16
JournalBiometrika
Volume107
Issue number2
DOIs
StatePublished - Jun 1 2020
Externally publishedYes

Keywords

  • Bayesian inference
  • Geometric numerical integration
  • Markov chain Monte Carlo
  • Measure-valued differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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